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We are less likely to see support of native docker-compose integration because pipelines API is a custom implementation of similar functionality, and also because possible security issues, but looks like more features are currently in development to implement more docker-compose-like features in this open issue.

UPDATE: added support for multi-container pipelines, as described in documentation

I have checked-in in my repo the ca.pem and cert.pem needed by docker-compose in the keys directory. The private key is saved base64encoded, as a secure variable in Bitbucket pipelines environment variables, so I just decode it and paste it to keys/key.pem in the pipeline as the first step.

Keep in mind that i used docker login after setting the enviroment variables for the remote host.